People protest in front of the U.S. Courthouse in Detroit during the city's bankruptcy eligibility trial.

When it comes to investment advice, you don't always get what you pay for. And when it comes to state pensions, it's not even clear how much those funds' advisors are getting paid.

That's the takeaway from a recent analysis of more than 70 large pension funds in all 50 states for fiscal 2014 by The Pew Charitable Trusts.

Unreported investment fees in 2014 were estimated at more than $4 billion, mostly payments to private equity managers, in addition to the $10 billion in reported investment expenses that year, the report shows.

The hidden fees and subpar performance are hitting more than just the retired teachers and state employees covered by public pensions. After more than a decade of underfunding, state pension funds are an estimated $1 trillion short of what they need to cover current and future obligations. Because those benefits are legally binding, taxpayers are ultimately on the hook to make up that shortfall.

As pension funds have fallen further behind their assumed investment returns, many have shifted funds into more risky alternative investment like private equity and hedge funds. That's largely due to the historically low interest rates of the last decade, which dramatically shrank the returns pension funds typically earned on safer, fixed income investments like bonds.

But those riskier investments come with higher fees, which have driven up costs for state pension funds. Overall, investment fees rose from 0.26 percent in 2006 to 0.34 percent in 2014. Though the percentage increase may seem small, that number represents more than $2 billion in annual fees.

And that only accounts for the fees that were reported in the funds' annual financial disclosures analyzed by the Pew researchers. They estimate that hidden fees could have topped $4 billion, more than 40 percent of the $10 billion in pension fund fees that were reported for 2014.

There's more than $3.6 trillion invested in state pension funds

Some states are pressing for fuller fee disclosures, including the California Public Employees Retirement System, which said in 2015 it would begin breaking out additional costs in its annual reports.

Higher fees don't seem to bring better investment returns, based on the report's data on one-, five- and 10-year returns. While the average fund in 2015 continued to assume a rate of return of more than 7.5 percent, the average real return was less than half that.

"Maintaining high expected rates of return reduces the size of annual payments into the plan from governments' budgets," the report said. But eventually, "state and local plan sponsors must make up for the shortfall."